Mathematica 11.0.1 has a habit of expressing real valued functions in terms of combinations of functions of a complex variable. This makes it difficult to see exactly how the function depends on the real valued variable for which it is defined.
An example that I have in mind is the function f(T) which is defined below. f is a real valued function and T is a dimensionless time which is also real.
f(T) is defined as Ei[2(Eulergamma) - i(pi) + ln[1/(4T)]] + Ei[2(Eulergamma) + i(pi) + ln[1/(4T)]].
Eulergamma is Euler's second constant which is approximately 0.5772, i is the complex number i, ln is the natural logarithm, and Ei is the Exponential Integral Ei function which is defined by Mathematica 11.0.1 as
Ei(z) = - Integral from (-z) to infinity of (e^(-t))/t dt.
If it can be shown how the above function f(T) can be written only in terms of real valued variables, I would be very grateful.
Thanks very much for your generous help,
Ron Zamir
Hi, I often use MAPLE for this kind of calculus and the same occurs (use of complex expressions). In this case, I try to compute the real part of the result when possible. Di you try this in MATHEMATICA ?
@Zamir
If you spell out your problem , then one can help you. If you agree then in pdf form.
e^(-t+i*pi))=-e^(-t)
e^(-t-i*pi))=-e^(-t)
Ei(z) = - Integral from (-z) to infinity of (e^(-t+i*pi))/(t-i*pi) dt=
= Integral from (-z) to infinity of (e^(-t))*(t+i*pi)/(t^2+pi^2) dt=
=Integral from (-z) to infinity of (e^(-t))*t/(t^2+pi^2) dt+
+i*Integral from (-z) to infinity of (e^(-t))*pi/(t^2+pi^2) dt
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